Homework QuestionsHomework Questions

Section 4.4Section 4.4

Graphing sin(x) and cos(x)Graphing sin(x) and cos(x)•Investigation FIRST!Investigation FIRST!•Input/Output discussionInput/Output discussion•Do sin(x) only to get Do sin(x) only to get started…started…

Periodic:Periodic:

A function is periodic if for some A function is periodic if for some real number real number αα, f (x+ , f (x+ αα) = f (x) for ) = f (x) for each x in the domain.each x in the domain.

The least positive value for The least positive value for αα for for which f (x+ which f (x+ αα) = f (x) is the ) = f (x) is the periodperiod of the function. of the function.

Examples…Examples…

Graph on your calc:Graph on your calc:

y = sin(x) and determine if y = sin(x) and determine if periodicperiodic

(ZOOM – TRIG)(ZOOM – TRIG)

Properties of sin(x)Properties of sin(x)

Period = 2Period = 2ππ Domain: (-∞, ∞)Domain: (-∞, ∞) Range: [-1, 1]Range: [-1, 1]

Graph cos xGraph cos x

On investigation sheet first…On investigation sheet first…

Graph cos xGraph cos x

Properties of cos(x)Properties of cos(x)

Period = 2Period = 2ππ Domain: (-∞, ∞)Domain: (-∞, ∞) Range: [-1, 1]Range: [-1, 1]

Section 4.4Section 4.4

Translating sin and cosTranslating sin and cos

AmplitudeAmplitude

The amplitude of the functions The amplitude of the functions

y = A sin y = A sin ӨӨ and and y = A cos y = A cos ӨӨ is the is the absolute value of A.absolute value of A.

Period = Period =

y = a sin (bx +c) + dy = a sin (bx +c) + d y = a cos (bx +c) + dy = a cos (bx +c) + d The distance it takes to go The distance it takes to go ““one one

wavewave””

b

2

State the amplitude State the amplitude and the period and and the period and graph:graph:

2

cos4

y

State the amplitude State the amplitude and the period and and the period and graph:graph:

4sin2

1y

State the amplitude State the amplitude and the period and and the period and graph:graph:

3

cos2

y

State the amplitude State the amplitude and the period and and the period and graph:graph:

xy 2sin2

3

One last thing…One last thing…

Write an equation of the Write an equation of the cosine function with amplitude cosine function with amplitude 9.8 and period 69.8 and period 6ππ..

HomeworkHomework

P. 394 (1-15 odd) - donP. 394 (1-15 odd) - don’’t graph, t graph, just state information (17-28) – just state information (17-28) – State all information and graph State all information and graph one period.one period.

Sticker assignment – posted Sticker assignment – posted onlineonline